Bart van Ingen Schenau’s answer is right in that UML is just a language and not a methodology. However, there are some methodologies that are built around tools (including UML), such as the Rational Unified Process. Different UML diagrams are used throughout the different phases of RUP.
It’s not really possible to specifically say how you can fit graphical modeling into your process without an understanding of your process. A sequential process is going to look different than an iterative and incremental process, for example. If you’re basing your methodology on the agile and lean principles, that will also guide how you can apply graphical modeling into your process.
In a sequential process, Activity, State, and Use Case diagrams will likely be the first created. These can be used to capture business processes and activities at a much higher level of abstraction than some of the other diagrams. You may also start to see abstract Class, Component, and Sequence diagrams to start to capture business relations, but these will evolve over time to be more detailed. The other diagrams are closer to the architecture and code and will be created as you define your architecture.
The exact diagrams that you create will depend on what you are trying to communicate and who you are trying to communicate with. There’s not much value in creating diagrams that don’t help someone understand the system under design or progress with work. There are also diagrams and modeling techniques that aren’t part of UML that could be useful.